Hardesty/Hardesty3
surface fitting problem (larger version)
Name 
Hardesty3 
Group 
Hardesty 
Matrix ID 
2833 
Num Rows

8,217,820 
Num Cols

7,591,564 
Nonzeros

40,451,632 
Pattern Entries

40,451,632 
Kind

Computer Graphics/Vision Problem 
Symmetric

No 
Date

2015 
Author

S. Hardesty 
Editor

T. Davis 
Structural Rank 
7,591,564 
Structural Rank Full 
true 
Num Dmperm Blocks

1 
Strongly Connect Components

1 
Num Explicit Zeros

0 
Pattern Symmetry

0% 
Numeric Symmetry

0% 
Cholesky Candidate

no 
Positive Definite

no 
Type

real 
Download 
MATLAB
Rutherford Boeing
Matrix Market

Notes 
Surface fitting problem for visualization, Sean Hardesty
Visualization of 3D structures in the earth
The Hardesty3 matrix is an interpolation matrix stacked above a
weighted Laplacian, to to fit a surface z(x,y) to a set of points
in R^3 subject to a smoothness constraint enforced via regularization.
Hardesty2 is a smaller version of this problem.
For the big matrix (Hardesty/Hardesty3), sparse QR (via SuiteSparseQR,
or SPQR) finds an R factor and a set of Householder vectors (Q.H) with
about 150 million nonzeros. Sparse LU factorization (with UMFPACK
v5.7.1) sees very high fillin (about 2.5 billion nonzeros in L+U).
The Hardesty1 matrix is a simple discretization of a 2D biharmonic
operator with some Lagrange multiplier constraints used for smoothing.
